Question

2)(2+x)(x-3)-3=(x+1)^24)(y-1)^2-(y+1)(y-7)=0​

Answer 1

Ответы на рисунке........

Answer 2

To solve the equation (2+x)(x-3)-3=(x+1)^2, we will follow these steps: Step 1: Expand the equation Step 2: Simplify and gather like terms Step 3: Solve for x Let's go through each step in detail: #### Step 1: Expand the equation To expand the equation, we need to multiply the terms using the distributive property. Let's expand both sides of the equation: On the left-hand side, we have: (2+x)(x-3) - 3 Using the distributive property, we multiply each term inside the parentheses with the terms outside the parentheses: 2(x) + 2(-3) + x(x) + x(-3) - 3 Simplifying this expression gives us: 2x - 6 + x^2 - 3x - 3 On the right-hand side, we have: (x+1)^2 Expanding this expression using the formula for squaring a binomial, we get: (x+1)(x+1) = x^2 + x + x + 1 = x^2 + 2x + 1 So the expanded equation becomes: 2x - 6 + x^2 - 3x - 3 = x^2 + 2x + 1 #### Step 2: Simplify and gather like terms Now, let's simplify and gather like terms on both sides of the equation: On the left-hand side, we have: 2x - 6 + x^2 - 3x - 3 Combining like terms gives us: x^2 - x - 9 On the right-hand side, we have: x^2 + 2x + 1 Since the equation is set to zero, we can rewrite it as: x^2 - x - 9 = 0 #### Step 3: Solve for x To solve the quadratic equation x^2 - x - 9 = 0, we can use factoring, completing the square, or the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula: The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by: x = (-b ± √(b^2 - 4ac)) / (2a) Comparing this with our equation x^2 - x - 9 = 0, we have: a = 1, b = -1, c = -9 Plugging these values into the quadratic formula, we get: x = (-(-1) ± √((-1)^2 - 4(1)(-9))) / (2(1)) x = (1 ± √(1 + 36)) / 2 x = (1 ± √37) / 2 So the solutions for x are: x = (1 + √37) / 2 x = (1 - √37) / 2 #### Solving the equation (y-1)^2 - (y+1)(y-7) = 0 To solve the equation (y-1)^2 - (y+1)(y-7) = 0, we will follow similar steps: Step 1: Expand the equation Step 2: Simplify and gather like terms Step 3: Solve for y Let's go through each step in detail: #### Step 1: Expand the equation To expand the equation, we need to multiply the terms using the distributive property. Let's expand both sides of the equation: On the left-hand side, we have: (y-1)^2 - (y+1)(y-7) Expanding the square (y-1)^2 gives us: (y-1)(y-1) = y^2 - y - y + 1 = y^2 - 2y + 1 Expanding the second term (y+1)(y-7) using the distributive property gives us: y(y) - y(7) + 1(y) - 1(7) = y^2 - 7y + y - 7 = y^2 - 6y - 7 So the expanded equation becomes: y^2 - 2y + 1 - (y^2 - 6y - 7) = 0 #### Step 2: Simplify and gather like terms Now, let's simplify and gather like terms on both sides of the equation: On the left-hand side, we have: y^2 - 2y + 1 - (y^2 - 6y - 7) Removing the parentheses gives us: y^2 - 2y + 1 - y^2 + 6y + 7 Combining like terms gives us: 4y + 8 On the right-hand side, we have: 0 So the equation simplifies to: 4y + 8 = 0 #### Step 3: Solve for y To solve the linear equation 4y + 8 = 0, we can isolate the variable y by subtracting 8 from both sides: 4y = -8 Dividing both sides by 4 gives us: y = -8/4 y = -2 So the solution for y is: y = -2 In summary, the solutions for the given equations are: For the equation (2+x)(x-3)-3=(x+1)^2: x = (1 + √37) / 2 x = (1 - √37) / 2 For the equation (y-1)^2 - (y+1)(y-7) = 0: y = -2